Game theory prescribes strategies based on reasoning that is often beyond the reach of bounded players. This book identifies when they can learn their way to equilibrium-and when they cannot.

Game theory traditionally assumes that players have no cognitive limits and fully know their strategic circumstances. Without those assumptions, equilibrium reasoning no longer guides their decisions. Existing approaches to bounded rationality-ecological rationality, epistemic game theory, evolutionary models, the learning-in-games tradition, and procedural rationality-offer no unified account of how players should learn in uncertain, changing environments or when learning converges to equilibrium.

Ashton T. Sperry-Taylor introduces strategic bandits, which model an opponent using a memory-m rule: the opponent's next move depends on the preceding m rounds. Decision policies have precise convergence conditions. Action-level learning succeeds when players identify the best fixed action and when conditional responses offer no additional value. At the strategic boundary, a conditional policy outperforms every fixed action, even when players learn the best one. At the estimation boundary, the learning process prevents players from identifying that best fixed action.

Sperry-Taylor develops his account through five games: the prisoner's dilemma, the centipede game, the stag hunt, divide the cake, and the battle of the sexes. Across them, bounded players learn their way to equilibrium, fail to coordinate because their payoff estimates mislead them, or learn more slowly to protect against an unpredictable opponent. He distinguishes between difficulties arising from the strategic situation and those arising from the learning process itself.